adjacent angles
Adjacent angles are a pair of angles that share a common vertex and a common side, but do not overlap
Adjacent angles are a pair of angles that share a common vertex and a common side, but do not overlap. In other words, they are angles that are next to each other. The shared side of adjacent angles forms a straight line.
When two adjacent angles are added together, the sum of their measures will always be 180 degrees, because they form a straight line. This property is known as the angle addition postulate.
For example, in the figure below, angle AOC and angle COB are adjacent angles. They share the common side OC and the common vertex O.
O
/ \
/ \
A/_____\B
\ /
\ /
\ /
C
The sum of the measures of angle AOC and angle COB will be 180 degrees. So, if angle AOC measures 70 degrees, angle COB will measure 110 degrees, since 70 + 110 = 180.
Adjacent angles are commonly found in geometric figures and can help in solving various mathematical problems, such as finding missing angles, proving theorems, or determining the relationships between angles in different shapes.
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